Reflectometry is the term given to the measurement technique where a transmitted signal waveform is directed at a surface and the reflected signal is then correlated with a copy of the transmitted signal to yield information about the characteristics of the reflecting surface.
Global Navigation Satellite System reflectometry (GNSS-R) uses a satellite in a low earth orbit to capture Global Navigation Satellite System (GNSS) signals reflected from the earth and to correlate each of these signals with either a locally generated replica of the transmitted signal or with the transmitted signal itself which has been received directly from the GNSS satellite.
In more detail, by correlating the received signal with a signal received directly from the GNSS satellite, the path difference between the paths traveled by the reflected and the direct signal can be determined. The correlation effectively involves sliding the transmitted waveform across the received waveform, one sample at a time, and at each position multiplying the signals, sample by sample, before adding the products to form a correlation sample. The position at which the correlation peak is found corresponds to the relative delay between the signals and therefore the path difference. Since the orbits of the two satellites are known, the path difference can be used to determine the height of the reflecting surface.
For example, GNSS-R can be used for oceanographic applications to map the sea surface and determine the height of the surface of the sea over time. The altitude of the satellite with respect to the standard earth World Geodetic System (WGS) ellipsoid is known from the orbit of the satellite and the reflectometry measurements give the height above the sea level. The difference between the altitude of the satellite with respect to the WGS ellipsoid and the height above the sea level corresponds to the sum of the sea height and the local geo potential height. The geopotential is not known with sufficient accuracy to compute the sea height above the geopotential but it is assumed to be fixed so differences in measurements taken over time can be attributed to changes in the sea height.
In many applications it also desired to determine the Doppler spreading of the reflected signal. The Doppler spread is the difference in Doppler shift between different components of the reflected signal. Accordingly, it is sometimes desirable to compute a delay Doppler map (DDM), which is a 3D surface of the received energy as a function of delay and Doppler shift.
It is known to use discrete fourier transforms (DFT) and inverse discrete fourier transforms (IDFT) to correlate two signals. It is also known that fast fourier transforms (FFT) are efficient algorithms for computing the discrete fourier transform and its inverse. However, FFTs are impractical to implement when the number of samples in a signal to be transformed is large. For example, in a GNSS-R system for an oceanographic application, the number of samples in the sampled reflected signal may be 100,000, which makes FFTs difficult to implement.
One conventional approach for computing a delay Doppler map is to frequency shift a copy of the direct signal by an amount corresponding to a possible Doppler frequency and then to correlate the reflected signal with the frequency shifted copy of the direct signal for a set of delays to give one DDM slice along the delay axis. This can then be repeated for each frequency shift of interest. The approach is most efficient if the number of delay lags K is much larger than the number of frequency shifts L in the DDM and an efficient FFT based technique is used to compute the delay lags
Another approach is to multiply each sample of the reflected signal with its corresponding delayed sample of a delayed copy of the direct signal and then to carry out an FFT on each lag sequence to compute the complete set of Doppler frequencies L for a specific delay. This can then be repeated for each delay. This approach is most efficient if the number of frequency shifts L of interest is much larger than the number of delay lags K. A problem with this approach is that an FFT may be impractical if the number of samples in each lag sequence is very large. Comb filters with output decimation have therefore been used to reduce the number of samples in each lag sequence.
In “An Improved Algorithm for High Speed Autocorrelation with Applications to Spectral Estimation, C. Rader, IEEE Transactions on Audio and Electroacoustics, Vol. AU-18, No. 4, December 1970, it is disclosed an FFT algorithm which involves using J-point cross correlations to correlate two sequences of length N, where J<<N.
The invention was made in this context.